The allegation that the 36-year-old was working for MI6 was made by an American investigative journalism website – The Intercept – in an article about SEAL Team 6, who killed al-Qaeda leader Osama bin Laden.
Ms Norgrove, from Uig on the Isle of Lewis, was killed in 2010 during a US military rescue following her kidnap by the Taleban in Kunar province.
Linda’s parents John and Lorna, described the allegation as “ludicrous and hurtful”.
Speaking to a national newspaper they said: “The people who have fabricated this story didn’t know Linda.
“We were very close to her and kept in touch every week by Skype. Linda was passionately against war, disliked the military with a vengeance and mostly sided with Afghans rather than Western governments.
“The suggestion that she was working for MI6 is ludicrous and hurtful.”